Infinite-horizon Linear Quadratic Path-Following

This paper proposes a path-following policy for linear systems subject to stochastic disturbances. The problem is framed as that of choosing both the control inputs and the trajectory’s speed to minimize an infinite-horizon expected quadratic cost taking into account the state and the input. The path is modeled by an exosystem. It is shown that certainty equivalence holds when the path is a straight line. The proposed path-following policy improves the cost of the optimal constant speed trajectory-tracking policy associated with the exosystem. This policy guarantees that the tracking error converges to zero in the absence of disturbances. Numerical examples highlight the advantages of the method with respect to trajectory-tracking.